プラタナス2 の山 12 月 3 週
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○The Complete Man(感) 英文のみのページ(翻訳用)
The Complete Man

After his marriage to Princess Elizabeth and following her accession to the throne as Queen Elizabeth ? in 1952, Prince Philip's many interests and his sympathetic understanding of present-day problems were reflected in the speeches he made on public occasions. The speech quoted here is characteristic of his clear vision and of his ability to combine courtesy and plain speaking.
In the Middle Ages it was the Church and the universities which were primarily responsible for knitting together the nations of Europe in a common culture. This amounted to a system of thought and behaviour, conditioned by a reverence for the classics and restrained by religion and social custom. Two world wars and the advent of science have completely upset those conditions and removed those restraints. So far we have neither returned to them nor put anything in their place. The responsibility of the universities is therefore much greater today if they are to minister to the specialized needs of modern society and to regain their position as the spiritual and moral reservoirs of Europe and the world.
One of the marks of the Middle Ages was the free movement of scholars from university to university across the face of Europe. Since then the world has grown much smaller and that mobility ought in our day to cover the whole world. Teachers in the arts must surely benefit from a wide personal knowledge of the places where those arts flourished most nobly, and the science teacher must surely draw inspiration from working in the universities which were responsible for some of the greatest strides in science. Perhaps even more important, the movement of teachers and students alike between universities must surely help to break down the narrow nationalism which grows up with isolation. A proper respect for the achievements of others may not be easy in this competitive world, but it is after all the first step towards a broad mind.
European culture, thought, and ideas have drifted all over the world, and although they have received some hard knocks in recent years there are many far-away places where people still believe that Europe has something good to offer. We shall have nothing to offer unless our behaviour, our ideals, and our achievements gain universal respect. We can only have something to offer if the universities have clearly before them what they are aiming to do.
With the inevitable growth of specialization I see the universities facing two great dangers. First, it is very easy to get so involved in the technical details of education that the object of education is lost. And secondly, in an effort to condition a university to the needs of its students and to the needs of the State it may lose its power to make or mould those students into reasonable and responsible men, capable of thinking for themselves and capable of expressing the result of their thoughts to others.
A university must do more than merely provide a high-class professional apprenticeship. It does not matter in the least what a student's specialized line happens to be; the fact that he is a specialist cannot excuse him from his responsibilities as a man. Students must emerge as complete human beings capable of taking their proper place in society as a credit to their universities both for their professional knowledge and as men. There is no conflict between the disciplines here. Nobody can be termed a complete man who has no knowledge of what science has to teach, and, equally, human obligations cannot be escaped on the grounds of being a specialized scientist or technologist.
By human obligations I mean the ability to behave in a reasonable way, to observe restraint so that restraints do not have to be imposed, to be able to think clearly and objectively so that false doctrines cannot gain ground. I believe that it also means the ability to see through nonsense, political, economic, scientific, and so on, and the feeling that it is a duty to resist it. This in no way conflicts with the amount of specialized knowledge, whether scientific, classical, or anything else, which the student can absorb and turn to good account for himself and the community at large.
The universities have a special responsibility to send people of that sort out into the world, because by their influence and example in the community at large they can extend the work of the universities to every corner of the world.
However, to produce the complete man with that balanced sense of obligation and understanding we need to know much more about man himself. Our knowledge of science, the classics, or medicine is beautifully documented, indexed, and ordered. We may not know everything about the subject, but what is known is neatly bound. I imagine that is why we sometimes call this an age of reason, but we forget that -- in the midst of all that reasonable knowledge -- man himself remains as unreasonable, irrational, and unpredictable as ever
Everything around us has been found to have laws and order, and there are some who faintly resent the fact that man refuses to be ordered in the same way. But we must take care not to treat man, with his immense variety of prejudices and emotions, as just another statistical unit. There is the conflict; and it is perhaps inclined to become most noticeable in scientists who deal with ordered things and thoughts in their professional lives, but when the problems are human ones it is not altogether surprising that their ideal solutions are not universally accepted. The reverse is, of course, also true. If you spend your life making compromises it is hard to understand why that is not possible in science.
I would like to repeat that the conflict is not between disciplines, between humanism and science. The conflict lies between man and the world he has made for himself. Man has succeeded in changing many things but he has not changed much himself. It is just because we have got such a grip on nature and such a store of knowledge for its own sake that we must remember the central character, man, and his possibilities, limitations, and the depths he can sink to if he relaxes his self-control.

Prince Philip, Duke of Edinburgh: from Selected Speeches (1955).

★絵画と音楽とが(感)
 【1】絵画と音楽とが二〇世紀にたどっていった道と数学の歩みとは、もしかすると重なり合うことがあるかもしれない。現代数学の抽象性をキュービズムや無調音楽となぞらえて捉えたくなっても不思議ではない面が確かにある。【2】数学的対象のもつある側面を取り出して強調すること、とくにひとつの対象のもつ種々の側面を現代数学の立場から説明することは、ひとつの対象をさまざまな角度から見たものをひとつのカンバスに描くピカソの絵とどこか似かよっている。【3】また、例えば個々の関数のもつ性質を一切無視してヒルベルト空間の元と捉えるところにしても、無調音楽に通じる無機的なものを感じることができよう。【4】さらに、長い長い抽象的な議論を経て結論へたどり着くことの多い現代数学の議論は非人間的だと思いたくなることもあるだろう。そうした意味で、絵画や音楽に現れた時代の影響を見て取ることができる。
 【5】しかしながら数学と音楽・絵画とは決定的に違う側面がある。それは数学のもつ普遍性である。数学の定理はひとたび証明されれば万人共通の真理となる。このことが過ぎると、カントの哲学のように数学の真理に対する誤った信頼さえ生じる。【6】われわれの住む空間はユークリッド幾何学の成立する空間であると頭から信じて哲学の基礎としたカントの強い影響力のもとで、非ユークリッド幾何学をガウスは用心深く隠す必要を感じていた。【7】数学者の無理解だけを恐れたのではなかったようである。われわれの住む空間の幾何学は物理の実験によって確かめることができるというリーマンの主張は、今日では当然のことと思われるが、当時は極めて勇気のいる主張でもあった。
 【8】こうした数学に対する信頼は今世紀に入って数学が抽象的になるにつれてなくなっていった。たとえばユークリッド幾何学に対する感覚的信頼と類似の感覚的信頼を現代数学に対して持つためにはそれなりの訓練が必要となる。【9】ユークリッド幾何学にしても複雑な定理は決して感覚的に自明なわけではなく、こみいった証明が必要になる。そうした意味では同じ面もあるが、基礎的な部分では∵間違いなく理論を感覚的に信頼することができる。【0】もっとも、古代ギリシャ人の偉大なところは感覚的な信頼を論理的な信頼に高めたところにある。ユークリッドの『原論』が長い間、学問の記述の手本とされたのもこうした点にある。しかしながら、論理的な信頼だけで最初から最後まで議論を押し通すことはかなりの忍耐を必要とし、通常は感覚的な助けが必要となる。
 今世紀に導入された数学上の基本的概念を最初に学ぶ際に理解しづらいのは、簡単には感覚的に捉えることが難しいことにも一因があるように思われる。訓練することによって一種の感覚が生まれてくるのであるが、そこに至る道には個人差が大きい。時として苦行を強いられるように感じられることもある。いずれにせよ、数学を美しいと感じることができなくては本当に数学が分かったという気にはなりにくいであろう。そこに至る道が困難な道であり、少数の人しか到達できないとすると、十二音技法の上手さに感心する作曲家や技術的な困難を克服して演奏するようになった演奏家と数学者とは近い存在ということになる。事実、パリティ非保存の法則の発見でノーベル賞を受賞した物理学者のヤンは、彼の学生であったミルズとともに創始したヤン―ミルズの理論が数学でのファイバー束の接続の理論と関係していると数学者に指摘され、この数学理論を勉強したときの感想を「現代数学者の言語は、物理学者にとってはあまりに冷たく抽象的だ。」と記している。
 こうした感想は現代数学を勉強した多くの人たちが共有するものであろう。こうした無機的なものを現代数学がもっていることは確かである。それを克服する道は、現代数学の基本的考え方を日常の言葉で表現する努力から始めるしかあるまい。それがどんなに困難であっても、数学が再び大きく飛躍するためには、避けて通れない道である。幸いにも現代数学は大きな内部運動をひとまず終了し、いま諸科学との交流のもとで新たな発展を見せつつある。二一世紀の数学が、数学の美しさ、楽しさを身近に感じさせてくれる学問へと深まっていくことを期待したい。

(上野健爾(けんじ)「誰が数学嫌いにしたのか」)